Question

if x+1/x =6 find value of x^2+1/x^2
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Answer 1

Answer:

• x² + 1/x² = 34

Given:

• x+1/x =6

To find:

• x² + 1/x²

Solution :

Formula used :

$\sf \underline{(a + b) {}^{2} + {a}^{2} + {b}^{2} = 2ab}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf{ : \implies \: {x}+ \dfrac{1}{ {x} }=\:6}$

Now squaring both sides we get,

$\: \: \ \: \: \: \: \sf{ : \implies \: ( {x}^{2} + \dfrac{1}{x} ) {}^{2} = {6}^{2} }$

• As we know that 6 × 6 = 36

$\: \: \: \: \: \: \sf{ : \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} } + 2(x) (\dfrac{1}{x}) = 36}$

$\: \: \: \: \: \: \sf{ : \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 36 - 2}$

$\: \: \: \: \: \: \sf{ : \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 34}$

$\sf \underline{(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab}$

$\sf \underline{ \therefore \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 34}$

More Explanation :

$\: \: \: \sf{ : \implies(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab}$

$\: \: \: \sf{ : \implies \: a {}^{2} - b {}^{2} = (a + b)(a - b)}$

$\: \: \: \sf{ : \implies(a - b) {}^{2} = {a}^{2} - {b}^{2} + 2ab}$

$\: \: \: \sf{ : \implies \: a {}^{3} + b {}^{3} = (a + b)( {a}^{2} - ab + {b}^{2)} }$

$\: \: \: \sf{ : \implies \: a {}^{3} - b {}^{3} = (a - b)( {a}^{2} + ab + {b}^{2)} }$

Answer 2

Answer:

Answer:

x² + 1/x² = 34

Given:

x+1/x =6

To find:

x² + 1/x²

Solution :

Formula used :

Now squaring both sides we get,

As we know that 6 × 6 = 36

More Explanation :

Step-by-step explanation:

Hope this answer will help you✌